Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

TL;DR

This paper analytically investigates stochastic resonance in bistable systems with anomalous diffusion, deriving key quantifiers and showing their dependence on diffusion parameters, enhancing understanding of such systems under periodic forcing.

Contribution

It provides an analytical formulation and derivation of stochastic resonance quantifiers in anomalously diffusing bistable systems, highlighting parameter dependencies.

Findings

Spectral amplification and SNR depend strongly on diffusion parameters.

Peak SNR occurs only within specific parameter ranges.

Analytical expressions for quantifiers are derived in the linear-response regime.

Abstract

The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker-Planck equation describing the system dynamics, together with the corresponding Ito-Langevin equation, are formulated. In the linear-response regime analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion, in particular the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.